15 August 2017, Volume 33 Issue 3
    

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  • ARTICLES
    New Discoveries of Domination Between Traffic Matrices
    Peng-fei LIU, Wen-guo YANG, Tian-de GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 561-566.
    DOI:10.1007/s10255-017-0636-7
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 + λ(D2 -D1) for any λ > 0 if D1 dominates D2. Let U(D) be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that U(D∞) and U(D∈) are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Furthermore, the results are the generalized to integral flows.
  • ARTICLES
    Some Comments on Zonal Polynomials and Their Expected Values with respect to Elliptical Distributions
    José A. Díaz-García, Ramón Gutiérrez-Jáimez
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 567-574.
    DOI:10.1007/s10255-011-0092-8
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    In this paper, we give alternative proofs of some results in[15] (Li R.,1997) about the expected value of zonal polynomials.
  • ARTICLES
    Asymptotic Behaviour of Hessian Equation with Boundary Blow Up
    Lei-na ZHAO, Zi-jian LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 575-586.
    DOI:10.1007/s10255-017-0683-0
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    We consider the boundary blow up problem for k-hessian equation with nonlinearities of power and of exponential type, and prove their existence, uniqueness and asymptotic behaviour. Moreover we also show that their perturbed problem has a unique positive solution, which satisfies some asymptotic behaviors to unperturbed problems under appropriate structure hypotheses for perturbed terms.
  • ARTICLES
    Uniform Exponential Attractors for Second Order Non-autonomous Lattice Dynamical Systems
    Xiao-peng ZHOU, Fu-qi YIN, Sheng-fan ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 587-606.
    DOI:10.1007/s10255-017-0684-z
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    In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, α-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.
  • ARTICLES
    On Total Colorings of Some Special 1-planar Graphs
    Lin SUN, Jian-liang WU, Hua CAI
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 607-618.
    DOI:10.1007/s10255-017-0667-0
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    A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △(G) ≥ 9 and g(G) ≥ 4, or △(G) ≥ 7 and g(G) ≥ 5, where △(G) is the maximum degree of G and g(G) is the girth of G.
  • ARTICLES
    An Influence Statistic For Linear Measurement Error Models
    Hadi EMAMI
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 619-632.
    DOI:10.1007/s10255-017-0682-1
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    Detection of multiple outliers or subset of influential points has been rarely considered in the linear measurement error models. In this paper a new influence statistic for one or a set of observations is generalized and characterized based on the corrected likelihood in the linear measurement error models. This influence statistic can be expressed in terms of the residuals and the leverages of linear measurement error regression. Unlike Cook's statistic, this new measure of influence has asymptotically normal distribution and is able to detect a subset of high leverage outliers which is not identified by Cook's statistic. As an illustrative example, simulation studies and a real data set are analysed.
  • ARTICLES
    Solving Multi-period Interdiction via Generalized Bender's Decomposition
    Maryam SOLEIMANI-ALYAR, Alireza GHAFFARI-HADIGHEH
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 633-644.
    DOI:10.1007/s10255-017-0687-9
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    This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.
  • ARTICLES
    Exact Inference for Joint Type-I Hybrid Censoring Model with Exponential Competing Risks Data
    SONG MAO, Yi-min SHI, Xiao-lin WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 645-658.
    DOI:10.1007/s10255-017-0688-8
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    Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates (MLEs) of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function (MGF). Confidence intervals (CIs) of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.
  • ARTICLES
    Non-selfsimilar Global Solutions and Their Structure for the Multi-dimensional Combustion Models
    Kai HU, Gao-wei CAO, Xiao-zhou YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 659-678.
    DOI:10.1007/s10255-017-0689-7
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    We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.
  • ARTICLES
    A Logarithmically Improved Regularity Criterion for the Supercritical Quasi-geostrophic Equations in Besov Space
    Sadek GALA
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 679-686.
    DOI:10.1007/s10255-017-0690-1
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    In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space Ḃ∞,∞-r(R2).The result shows that if θ is a weak solutions satisfies
    ∫0T((‖▽θ(.,s)‖Ḃ∞,∞-r(α/(α-r)))/(1+ln(e+‖▽┴θ(.,s)‖L(2/r)))ds<∞ for some 0 < r < α and 0 < α < 1,
    then θ is regular at t=T. In view of the embedding L(2/r)⊂M(2/r)p⊂Ḃ∞,∞-r with 2 ≤ p < (2/r) and 0 ≤ r < 1, we see that our result extends the results due to[20] and[31].
  • ARTICLES
    A Filter Line Search Algorithm Based on an Inexact Newton Method for Nonconvex Equality Constrained Optimization
    Zhu-jun WANG, De-tong ZHU, Cun-yun NIE
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 687-698.
    DOI:10.1007/s10255-017-0691-0
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    We propose an inexact Newton method with a filter line search algorithm for nonconvex equality constrained optimization. Inexact Newton's methods are needed for large-scale applications which the iteration matrix cannot be explicitly formed or factored. We incorporate inexact Newton strategies in filter line search, yielding algorithm that can ensure global convergence. An analysis of the global behavior of the algorithm and numerical results on a collection of test problems are presented.
  • ARTICLES
    High Accuracy Analysis of the Lowest Order H1-Galerkin Mixed Finite Element Method for Nonlinear Sine-Gordon Equations
    Dong-yang SHI, Fen-ling WANG, Yan-min ZHAO
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 699-708.
    DOI:10.1007/s10255-017-0692-z
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    The lowest order H1-Galerkin mixed finite element method (for short MFEM) is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order RaviartThomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O(h2)/O(h2 + τ2) in H1-norm and H(div; Ω)-norm are deduced for the semi-discrete and the fully-discrete schemes, where h, τ denote the mesh size and the time step, respectively, which improve the results in the previous literature.
  • ARTICLES
    Edge Coloring of Graphs Embedded in a Surface of Nonnegative Characteristic
    Yi-qiao WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 709-716.
    DOI:10.1007/s10255-017-0693-y
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    Let G be a graph embeddable in a surface of nonnegative characteristic with maximum degree six. In this paper, we prove that if G contains no a vertex v which is contained in all cycles of lengths from 3 to 6, then G is of Class 1.
  • ARTICLES
    M-estimation for Periodic GARCH Model with High-frequency Data
    Peng-ying FAN, Si-xin WU, Zi-long ZHAO, Min CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 717-730.
    DOI:10.1007/s10255-017-0694-x
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    This paper studies an M-estimator of a proxy periodic GARCH (p, q) scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.
  • ARTICLES
    Asymptotic Expansions for Solutions of Parabolic Systems Associated with Multi-scale Switching Diffusions
    Ky TRAN, G. YIN
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 731-752.
    DOI:10.1007/s10255-017-0695-9
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    This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuoustime Markov chain. In the model, there are two small parameters ε and δ. The first one highlights the fast switching, whereas the other delineates the slow diffusion. Assuming that ε and δ are related in that ε=δγ, our results reveal that different values of γ lead to different behaviors of the underlying systems, resulting in different asymptotic expansions. Although our motivation comes from stochastic problems, the approach is mainly analytic and is constructive. The asymptotic series are rigorously justified with error bounds provided. An example is provided to demonstrate the results.
  • ARTICLES
    ESL-SELO:A Robust Image Denoising Algorithm with Penalty
    Guo-hua WANG, San-guo ZHANG, Peng-jie DAI
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 753-770.
    DOI:10.1007/s10255-017-0696-8
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    Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method (ESL-SELO) to recover nosing image, which combine exponential loss function and seamless-L0 (SELO) penalty function to guarantee both accuracy and robustness of the estimator. Theoretical result showed that our method has a local optimal solution and good asymptotic properties. Finally, we compare our method with other methods in simulation which shows better robustness and takes much less time.
  • ARTICLES
    A New Infeasible-Interior-Point Algorithm for Linear Programming over Symmetric Cones
    Chang-he LIU, You-lin SHANG, Ping HAN
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 771-788.
    DOI:10.1007/s10255-017-0697-7
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    In this paper we present an infeasible-interior-point algorithm, based on a new wide neighbourhood N(τ1, τ2, η), for linear programming over symmetric cones. We treat the classical Newton direction as the sum of two other directions. We prove that if these two directions are equipped with different and appropriate step sizes, then the new algorithm has a polynomial convergence for the commutative class of search directions. In particular, the complexity bound is O(r1.5 log ε-1) for the Nesterov-Todd (NT) direction, and O(r2 log ε-1) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and ε > 0 is the required precision. If starting with a feasible point (x0, y0, s0) in N(τ1, τ2, η), the complexity bound is O(√r log ε-1) for the NT direction, and O(r log ε-1) for the xs and sx directions. When the NT search direction is used, we get the best complexity bound of wide neighborhood interior-point algorithm for linear programming over symmetric cones.
  • ARTICLES
    On Heavy Paths in 2-connected Weighted Graphs
    Bin-long LI, Sheng-gui ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 789-798.
    DOI:10.1007/s10255-017-0698-6
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    A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.
  • ARTICLES
    The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis
    Chen-qing CAI, Qian XU, Xiao-lin LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 799-808.
    DOI:10.1007/s10255-016-0500-1
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    Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.
  • ARTICLES
    Learning Dynamic Causal Relationships Among Sugar Prices
    Jing XU, Xing-wei TONG, Fang WANG, Jian-ping CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 809-818.
    DOI:10.1007/s10255-017-0699-5
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market (ZC), spot sugar price in Zhengzhou (ZS) and futures sugar closing price in New York futures exchange market(NC) and the other includes futures sugar opening price in Zhengzhou (ZO), ZS and NC. For each quarter, we first use Bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use Bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.
  • ARTICLES
    Backbone Coloring for Triangle-free Planar Graphs
    Yue-hua BU, Shui-ming ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 819-824.
    DOI:10.1007/s10255-017-0700-3
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let G be a graph and H a subgraph of G. A backbone-k-coloring of (G, H) is a mapping f:V (G) → {1, 2, …, k} such that|f(u) -f(v)| ≥ 2 if uv ∈ E(H) and|f(u) -f(v)| ≥ 1 if uv ∈ E(G)\E(H). The backbone chromatic number of (G, H) denoted by χb(G, H) is the smallest integer k such that (G, H) has a backbone-k-coloring. In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad(G) < 3, then there exists a spanning tree T of G such that χb(G, T) ≤ 4.
  • ARTICLES
    Piecewise w∞-equitable Efficiency in Multiobjective Programming
    D. FOROUTANNIA, A. MAHMODINEJAD
    Acta Mathematicae Applicatae Sinica(English Series). 2017, 33(3): 825-836.
    DOI:10.1007/s10255-017-0686-x
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of wr-equitable efficiency, where w ∈ R+m is a weight vector. First some theoretical and practical aspects of Pwr-equitably efficient solutions are discussed and by using the concept of Pwr-equitable efficiency one model is presented to coordinate weakly wr-equitable efficient solutions of subproblems. Then the concept of Pw∞-equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.
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